Practical Mathematical Optimization: Basic Optimization Theory and Gradient-Based Algorithms

It is intended that this book be used in senior- to graduate-level semester courses in optimization, as offered in mathematics, engineering, com- puter science and operations research departments. Hopefully this book will also be useful to practising professionals in the workplace. The contents of the book represent the fundamental optimization mate- rial collected and used by the author, over a period of more than twenty years, in teaching Practical Mathematical Optimization to undergradu- ate as well as graduate engineering and science students at the University of Pretoria. The principal motivation for writing this work has not been the teaching of mathematics per se, but to equip students with the nec- essary fundamental optimization theory and algorithms, so as to enable them to solve practical problems in their own particular principal fields of interest, be it physics, chemistry, engineering design or business eco- nomics. The particular approach adopted here follows from the author’s own personal experiences in doing research in solid-state physics and in mechanical engineering design, where he was constantly confronted by problems that can most easily and directly be solved via the judicious use of mathematical optimization techniques. This book is, however, not a collection of case studies restricted to the above-mentioned specialized research areas, but is intended to convey the basic optimization princi- ples and algorithms to a general audience in such a way that, hopefully, the application to their own practical areas of interest will be relatively simple and straightforward.

Jan A. Snyman currently holds the position of emeritus professor in the Department of Mechanical and Aeronautical Engineering of the University of Pretoria, having retired as full professor in 2005. He has taught physics, mathematics and engineering mechanics to science and engineering students at undergraduate and postgraduate level, and has supervised the theses of 26 Masters and 8 PhD students. His research mainly concerns the development of gradient-based trajectory optimization algorithms for solving noisy and multi-modal problems, and their application in approximation methodologies for the optimal design of engineering systems. He has authored or co-authored 89 research articles in peer-reviewed journals as well as numerous papers in international conference proceedings.

Daniel N. Wilke is a senior lecturer in the Department of Mechanical and Aeronautical Engineering of the University of Pretoria. He teaches computer programming, mathematical programming and computational mechanics to science and engineering students at undergraduate and postgraduate level. His current research focuses on the development of interactive design optimization technologies, and enabling statistical learning (artificial intelligence) application layers, for industrial processes and engineering design. He has co-authored over 50 peer-reviewed journal articles and full length conference papers.